Hexagon cut pyramid

Calculate the volume of a regular 6-sided cut pyramid if the bottom edge is 30 cm, the top edge is 12 cm, and the side edge length is 41 cm.

Correct answer:

V =  44790.6808 cm³

Step-by-step explanation:

$$\begin{gathered} a_1=30\text{ cm } \\ {a}_2=12\text{ cm } \\ s=41\text{ cm } \\ n=6 \\ {S}_1=n\cdot \sqrt{3}\mathrm{/}4\cdot a_1^2=6\cdot \sqrt{3}\mathrm{/}4\cdot 30^2=1350\sqrt{3}{\text{cm}}^2\doteq 2338.2686{\text{cm}}^2 \\ {S}_2=n\cdot \sqrt{3}\mathrm{/}4\cdot a_2^2=6\cdot \sqrt{3}\mathrm{/}4\cdot 12^2=216\sqrt{3}{\text{cm}}^2\doteq 374.123{\text{cm}}^2 \\ x=\sqrt{s^2-(a_1-a_2{)}^2}=\sqrt{41^2-(30-12{)}^2}=\sqrt{1357}\text{ cm}\doteq 36.8375\text{ cm } \\ {h}_2=x\cdot a_2\mathrm{/}(a_1-a_2)=36.8375\cdot 12\mathrm{/}(30-12)\doteq 24.5583\text{ cm } \\ {h}_1=x+h_2=36.8375+24.5583\doteq 61.3958\text{ cm } \\ {V}_1=S_1\cdot h_1\mathrm{/}3=2338.2686\cdot 61.3958\mathrm{/}3\doteq 47853.2914{\text{cm}}^3 \\ {V}_2=S_2\cdot h_2\mathrm{/}3=374.123\cdot 24.5583\mathrm{/}3\doteq 3062.6107{\text{cm}}^3 \\ V=V_1-V_2=47853.2914-3062.6107=44790.6808{\text{cm}}^3=4.479\cdot 10^4{\text{cm}}^3 \end{gathered}$$

Try another example

Related math problems and questions:

• Hexagonal pyramid
  Calculate the volume and the surface of a regular hexagonal pyramid with a base edge length of 3 cm and a height of 5 cm.
• Quadrangular pyramid
  Calculate the surface area and volume of a regular quadrangular pyramid: sides of bases (bottom, top): a1 = 18 cm, a2 = 6cm angle α = 60 ° (Angle α is the angle between the sidewall and the base plane.) S =? , V =?
• Hexagonal pyramid
  Find the volume of a regular hexagonal pyramid, the base edge of which is 12 cm long and the side edge 20 cm.
• Regular quadrilateral pyramid
  Find the volume and surface of a regular quadrilateral pyramid if the bottom edge is 45 cm long and the pyramid height is 7 cm.
• 9-gon pyramid
  Calculate the volume and the surface of a nine-sided pyramid, the base of which can be inscribed with a circle with radius ρ = 7.2 cm and whose side edge s = 10.9 cm.
• Truncated pyramid
  Find the volume of a regular 4-sided truncated pyramid if a1 = 14 cm, a2 = 8 cm and the angle that the side wall with the base is 42 degrees
• Quadrangular pyramid
  The regular quadrangular pyramid has a base length of 6 cm and a side edge length of 9 centimeters. Calculate its volume and surface area.
• Tetrahedral pyramid
  It is given a regular tetrahedral pyramid with a base edge of 6 cm and the height of the pyramid 10 cm. Calculate the length of its side edges.
• Tetrahedral pyramid
  A regular tetrahedral pyramid is given. Base edge length a = 6.5 cm, side edge s = 7.5 cm. Calculate the volume and the area of its face (side area).
• Triangular pyramid
  A regular tetrahedron is a triangular pyramid whose base and walls are identical equilateral triangles. Calculate the height of this body if the edge length is a = 8 cm
• Hexagonal pyramid
  Please calculate the height of a regular hexagonal pyramid with a base edge of 5cm and a wall height of w = 20cm. Please sketch a picture.
• Base diagonal
  In a regular 4-sided pyramid, the side edge forms an angle of 55° with the base's diagonal. The length of the side edge is eight meters. Calculate the surface area and volume of the pyramid.
• Pyramid
  The pyramid has a base rectangle with a = 6cm, b = 8cm. The side edges are the same and their length = 12.5 cm. Calculate the surface of the pyramid.
• Tetrahedron
  Calculate height and volume of a regular tetrahedron whose edge has a length 6 cm.
• Regular quadrilateral pyramid
  What is the volume of a regular quadrilateral pyramid if its surface is 576 cm² and the base edge is 16 cm?
• Hexagon area
  The center of the regular hexagon is 21 cm away from its side. Calculate the hexagon side and its area.
• Wall height
  Calculate the height of a regular hexagonal pyramid with a base edge of 5 cm and a wall height w = 20 cm.